Method and apparatus of plasma flow control for drag reduction

ABSTRACT

A plasma plate is used to minimize drag of a fluid flow over an exposed surface. The plasma plate includes a series of plasma actuators positioned on the surface. Each plasma actuator is made of a dielectric separating a first electrode exposed to a fluid flow and a second electrode separated from the fluid flow under the dielectric. A pulsed direct current power supply provides a first voltage to the first electrode and a second voltage to the second electrode. The series of plasma actuators is operably connected to a bus which distribute powers and is positioned to minimize flow disturbances. The plasma actuators are arranged into a series of linear rows such that a velocity component is imparted to the fluid flow.

CROSS REFERENCE TO RELATED APPLICATION

This application is a non-provisional claiming priority to U.S. PatentApplication No. 62/367,279 entitled “Novel Method Of Plasma Flow Controlfor Drag Reduction,” filed previously on Jul. 27, 2016, the contents ofwhich are incorporated herein by reference in their entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under Grant Number#NNX15CL65P awarded by NASA. The government has certain rights in theinvention.

FIELD OF THE DISCLOSURE

The present description relates generally to a pulsed direct currentpowering system for a dielectric barrier discharge (DBD) plasma actuatorfor flow control.

BACKGROUND OF RELATED ART

It is known that improving fuel efficiency is an ongoing goal for bothgovernment and industry, both within the United States andinternationally. Fuel costs have historically been the largest singlecost associated with aircraft operations; improved efficiency thereforetranslates directly to the bottom line. The worldwide aviation industryis a significant emitter of carbon dioxide and other greenhouse gases;the International Civil Aviation Organization (ICAO) puts it at 2% ofthe global anthropogenic total. The impact of these emissions isamplified even more, however, because they go directly into the uppertroposphere. Both Government regulators and industry associations haveset aggressive goals for reducing these emissions, but these willrequire significant new technology. An effective drag-reducing techniquewill directly assist in reducing fuel consumption, and hence reduce fuelexpenses and greenhouse gas emissions.

It is well known that streamwise vorticity dominates near-wallturbulence production and skin friction drag. As such, efforts tointervene in the self-sustaining mechanism of streamwise vortexformation and instability will yield drag reduction. Prior researchdescribed a new mechanism for coherent structure generation in theself-sustaining mechanism of near-wall turbulence. Their resultsstrongly suggest that normal mode low-speed streak instability is not asignificant contributor to streamwise vortex growth and near-wallturbulence production. Rather, they proposed and demonstrated a new“Streak Transient Growth Instability” (STGI) as the dominant streamwisevortex generation mechanism. Their work showed that STGI can produceorder-of-magnitude linear growth of streamwise disturbances.

Other works, based on direct numerical simulations of channel flow, haveproposed a strategy for drag reduction by actively intervening in theSTGI process. In particular, they found that streamwise coherentstructures in near-wall turbulence are created by the sinuousinstability of lifted vortex-free streaks due to the presence ofprevious vortices. They proposed a method of large-scale flow controlfor drag reduction, which exploits the fact that the low-speed streakgrowth rate depends critically on the wall-normal vorticity, ω_(y),flanking the streak as shown in FIG. 1. This figure presents theinstability growth rate as a function of wall normal vorticity andclearly delineates regions of stability and instability based on themagnitude of ω_(y).

The authors demonstrate that control schemes based on decreasing ω_(y)are successful in achieving very significant drag reduction (e.g. up to50% in their channel flow DNS). They found that control in the form ofeither spanwise colliding wall jets or an array of 2D counter-rotatingvortices was able to break the cycle of near-wall vortex generation bydisrupting the unstable streak distribution due to older, preexistingstreamwise vortices. Their approach has the advantage of achievingdistributed flow control without the need for any flow sensors orsupporting control logic.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a chart showing the prior art showing the dependence of sinousstreak instability growth rate on streak flanking wall-normal vorticity.

FIG. 2 is a photograph of the Notre Dame Mach 0.6 wind tunnel.

FIG. 3A is a schematic drawing of the wind tunnel shown in FIG. 2.

FIG. 3B is an end view of the schematic drawing of the wind tunnel ofFIG. 3A.

FIG. 3C is a top view of the schematic drawing of the wind tunnel ofFIG. 3A.

FIG. 3D is a detailed view of the schematic drawing of the wind tunnelof FIG. 3A.

FIG. 4 is a photograph of the removable aluminum panel with a testhard-wall liner coupon located in the center.

FIG. 5 is a photograph of a pair of linear air bearings used in the windtunnel test section.

FIG. 6 is a schematic illustration of a DB DBD plasma actuator.

FIG. 7 is a photograph of the an example of a plasma actuator circuitaccording to teachings of this disclosure.

FIG. 8A is a chart showing the voltage time series measuring at thecovered electrode.

FIG. 8B is a chart showing the voltage time series measuring at theexposed electrode.

FIG. 9 is a chart of induced thrust from the AC and DC DBD plasmaactuator

FIG. 10 is a table of the boundary layer parameters.

FIG. 11A is a photograph of the setup used to measure the velocity fieldinduced by the plasma actuator.

FIG. 11B is another photograph of the setup used to measure the velocityfield induced by the plasma actuator shown in FIG. 11A.

FIG. 12A is a graphical depiction of the mean induced velocity of theplasma actuator 4 mm from the exposed electrode.

FIG. 12B is a graphical depiction of the mean induced velocity of theplasma actuator 24 mm from the exposed electrode.

FIG. 13A is a graph of the peak induced velocity as a function ofdistance from the exposed electrode.

FIG. 13B is a graph of the distance of the peak induced velocity as afunction of distance from the exposed electrode.

FIG. 14A is an example embodiment of a plasma plate according to theprinciples of this disclosure.

FIG. 14B is an example embodiment of a plasma plate according to theprinciples of this disclosure.

FIG. 15A is a photograph of the example embodiment of the plasma plate.

FIG. 15B is another photograph of the example embodiment of the plasmaplate operating.

FIG. 16 is a photograph of the example embodiment of the plasma plate inthe wind tunnel.

FIG. 17A is a table of the configurations of the plasma plate showingthe electrode location.

FIG. 17B is a table of the configurations of the plasma plate showingthe pulse duty width cycle.

FIG. 17C is a table of the configurations of the plasma plate showingthe power input.

FIG. 17D is a table of the configurations of the plasma plate showingnet power benefit as Mach number increases.

FIG. 18 is a chart of baseline drag measurements without flow control asa function of freestream drag number.

FIG. 19A is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 16 mm opposed electrode.

FIG. 19B is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 16 mm opposed electrode.

FIG. 20 is a graph showing the percent change in drag reduction as afunction of vicious wall units for the 16 mm opposed electrode.

FIG. 21A is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 24 mm opposed electrode.

FIG. 21B is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 24 mm opposed electrode.

FIG. 22 is a graph showing the percent change in drag reduction as afunction of visious wall units for the 24 mm opposed electrode.

FIG. 23A is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 16 mm unidirectional electrode.

FIG. 23B is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 16 mm unidirectional electrode.

FIG. 24 is a graph showing the percent change in drag reduction as afunction of visious wall units for the 16 mm unidirectional electrode.

FIG. 25A is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 24 mm unidirectional electrode.

FIG. 25B is a graph showing the percent change in drag reduction for theuntripped ZPG TBL for the 24 mm unidirectional electrode.

FIG. 26 is a graph showing the percent change in drag reduction as afunction of visious wall units for the 24 mm unidirectional electrode.

FIG. 27 is a graph showing the optimal power savings for the opposedwall jet configuration.

FIG. 28 is a chart showing the net power savings of the 16 mm opposedelectrode configuration operating at 6 kV.

FIG. 29 is a chart showing the net power savings of the 24 mm opposedelectrode configuration.

FIG. 30 is a chart showing the net power savings of the 16 mm opposedelectrode configuration operating at 5 kV.

FIG. 31 is a chart showing the body force contours of a singleactuator's input.

FIG. 32 is a plot showing the pattern of the wall-normal velocityinduced by the plasma body forces arranged in an opposing-pairconfiguration after a short simulation in other quiescent.

FIG. 33 is a plot showing the pattern of the spanwise velocity inducedby the plasma body forces arranged in an opposing-pair configurationafter a short simulation in other quiescent.

FIG. 34 is a chart of the mean spanwise velocity profiles at varioustimes in the plasma-on turbulent channel slow simulation.

FIG. 35 is a chart profiles of the RMS of the streamwise velocitycomponent fluctuations across the channel at various times in theplasma-on simulation.

FIG. 36 is u-v fluctuation correlation profiles across the channel atvarious times in the baseline simulation.

FIG. 37 is a plot of the effects of the plasma body force on velocityfluctuations in the near-wall region where the plasma is active.

FIG. 38 is a depiction of the contours of the difference between thewall-normal velocity in the baseline case and the plasma-on case.

FIG. 39 is a depiction of the contours of the difference between thespanwise velocity in the baseline case and the plasma-on case.

FIG. 40 is a chart of the iso-surfaces of the positive (red) andnegative (cyan) streamwise velocity.

DETAILED DESCRIPTION

The following description of example methods and apparatus is notintended to limit the scope of the description to the precise form orforms detailed herein. Instead the following description is intended tobe illustrative so that others may follow its teachings.

In this disclosure, it is achieved significant skin friction dragreduction in self-sustaining, fully turbulent, wall bounded flows byimplementing large-scale, smart, active flow control at the wall, whichserves to intervene in the STGI mechanism. The disclosed plasma arrayachieves this effect by imparting a velocity component to a fluid. Theplasma array is (shown in FIGS. 14A-15B) uses a ordered series of plasmaactuators (shown in FIG. 6) to control the vorticity of the fluid flowaround the wall. This is termed revolutionary new flow controltechnology “Smart Longitudinal Instability Prevention via PlasmaSurface” or SLIPPS which is discussed in more detail below.

In this disclosure, it is demonstrated, both experimentally andnumerically, the viability of the SLIPPS flow control method to reducedrag. This demonstration is focused on a flat plate experimentalconfiguration at low Mach number. The corresponding simulations are of afully developed channel flow at a higher Mach number, but with theReynolds number reduced in order to enable resolution of all theimportant unsteady scales of motion.

The objectives of the this disclosure are, therefore, to demonstratethat: 1) A plasma-based approach can intervene successfully in the STGImechanism and create meaningful drag reduction. 2) Numerical simulationscan resolve the same physics and predict the drag reducing effects ofplasma intervention in the STGI mechanism.

The disclosure was validated in the Notre Dame Mach 0.6 wind tunnel 30.A photograph of the wind tunnel used to verify this disclosure is shownin FIG. 2. This is a low-disturbance closed return wind tunnel withfree-stream air temperature control. The test section dimensions are 1 mby 1 m cross-section by 3 m long. The Mach number range in the testsection is from 0.05 to 0.6. The air temperature range in the testsection is 32° C. to 60° C. The test section is designed with threeremovable and fully interchangeable windows on all four sides. Thewindows can be replaced with panels that can be specifically designedfor different experiments. A schematic of the test section shown inFIGS. 3A-3D illustrates how panels are used in window openings to act ashard points for the installation of various test articles. The testarticle in the schematic is a NASA Energy Efficient Transport (“EET”)airfoil section. The airfoil in this schematic is mounted on a pair offorce plates that ride on linear bearings. The same concept was used tomeasure drag on the test plate in the present experiment.

A 9 in. by 9 in. test plate was located in the center of a removableAluminum panel that was placed in one of the window locations in thetest section. This test plate was either a smooth hard surface, or oneof the plasma actuator covered surfaces. The Aluminum panel was machinedto a high tolerance so that the gap around the test plate was no morethan 0.020 in.

The test plate was mounted on a pair of linear air bearings that weremounted under the Aluminum panel. The connection to the test plate wasadjustable at four points so that the flow-side surface of the testplate could be made to be flush to within ±0.01 O in. of the insidesurface of the surrounding Aluminum panel.

A photograph of the smooth test plate located in the center of theAluminum panel is shown in FIG. 4. A photograph of the linear airbearing system that supports the test plate is shown in FIG. 5. In thepresent experiments, the Aluminum panel in which the plasma test platewas held was located in the most downstream position in the test sectionfloor. This provided the thickest naturally developing turbulentboundary layer, and x-Reynolds number, at the plasma test platelocation.

In addition to the naturally developing turbulent boundary layer, aboundary layer trip consisting of a 0.25 in. thick bar that spanned thetest section, was used to produce a thicker turbulent boundary layer atthe panel location. The mean velocity profiles of the two boundary layercases just upstream of the plasma panel were documented with a Pitotstatic probe mounted to a traversing mechanism.

The air bearings supporting the plasma test plate were aligned in themean flow direction. They provide a friction-less motion that wasresisted by a translation load cell. The load cell thus measure theaerodynamic force (drag) that was exerted on the test plate. For thevelocity range used in the experiments, a load cell with a maximumrating of 0.5 N (50 gm.) was selected. The load cell is an SMD S100,which according to the manufacturer has a hysteresis of 0.05% of ratedoutput (R₀=50 gm.) and a non-repeatability of 0.05% of R₀. Summing theseerrors, the total possible error is 0.08% of RO or approximately 0.04gm. For the range of Mach numbers expected to be from approximately 3.05gm. to 12.2 gm. Therefore, the maximum uncertainty in the dragmeasurements was approximately 1% of 0.05 to 0.1 utilized in theexperiments, the drag force on the 9 in. by 9 in. test panel wasexpected to be from approximately 3.05 gm to 12.2 gm. Therefore, themaximum uncertainty in the drag measurements was approximately 1%.

The Mach number in the test section was monitored using a Pitot-staticprobe and a temperature sensor located at the entrance to the testsection. Their readings were fed back to the wind tunnel control systemto maintain a constant condition. The voltages proportional to thetemperature, pressures and drag force were acquired through adigital-to-analog converter in a digital data acquisition computer thatoperated in a Matlab environment. These voltages were converted back tophysical quantities using pre-determined calibration relations.

In this disclosure, it is demonstrated over 65% drag reduction using theinnovative SLIPPS concept. A new powering system for dielectric barrierdischarge (DBD) plasma actuators that utilizes a pulsed-DC waveform wasused to operate the plasma panels. Per experimental evidence of thebreakthrough performance in drag reduction achieved in Phase I, it isbelieved that this revolutionary new actuator offers tremendouspotential as a practical drag reduction device for air vehicles.

Referring now to the figures, FIG. 6 shows an example prior art AC-DBDplasma actuator 10 including a pair of electrodes 102 and 104, adielectric 106, and a power source 112. The electrodes 102 and 104 areseparated by dielectric 106 but both electrically connected to the powersource 112 which is capable of producing an AC waveform. The electrodes102 and 104 are supplied with an AC voltage from the power source 112that causes the air over the covered electrode to ionize. The ionizedair, in the presence of the electric field produced by the geometry ofelectrodes 102 and 104, results in a body force vector field that actson the ambient (non-ionized, neutrally charged) air or other fluid. Thebody force can be used as a mechanism for active aerodynamic control.

As shown in the schematic for the pulsed-DC plasma actuator 20 in FIG.6, the DC voltage source 212 is electrically connected to both theexposed electrode 202 and the lower electrode 204. Between theelectrodes, the resistor 208 limits the current to the lower electrode204, which is also connected to a fast-acting solid-state switch 210.The solid-state switch 210, when closed, shorts the voltage to the lowerelectrode to the power supply ground from the DC voltage originallysupplied. A periodic trigger signal consisting of atransistor-transistor logic (TTL) pulse is supplied to activate thesolid-state switch 210 to deliver the micro-pulses to the electrodes202, 204. This can be accomplished by an external controller or aninternal signal generator. The pulse formed by the DC waveform producedby voltage source 212 and solid state switch 212 is a square wave with afloor of 0 V and a ceiling of the output voltage of voltage source 212.In other examples, the pulse could be varied with frequency modulationto include different pulses lengths, and the DC waveform could also beconstructed to regulate and control the voltage at either electrode 202,204.

A Pulsed-DC plasma actuator configuration is used similarly to the mosttypical AC-DBD designs. However, instead of an AC voltage input to drivethe actuator, the pulsed-DC utilizes a DC voltage source. The DC sourceis supplied to both electrodes, and remains constant in time for theexposed electrode. The DC source for the covered electrode isperiodically grounded for very short instants on the order of 10⁻⁵seconds. This process results in a plasma actuator body force that isthree-times larger than that with an AC-DBD at the same voltages. Moreimportantly, this new approach offers more controls on the body forcethat can potentially help to limit the effect to the sublayer region ofthe turbulent boundary layer.

The predominant DBD configuration used for flow control consist of twoelectrodes, one uncoated and exposed to the air and the otherencapsulated by a dielectric material. For plasma actuator applications,the electrodes are generally arranged in a highly asymmetric geometry.An example configuration is shown in the left part of FIG. 6. For theAC-DBD operation, the electrodes are supplied with an AC voltage that athigh enough levels, causes the air over the covered electrode to weaklyionize. The ionized air, in the presence of the electric field producedby the electrode geometry, results in a body force vector field thatacts on the ambient (non-ionized, neutrally charged) air. The body forceis the mechanism for active aerodynamic control. In determining theresponse of the ambient air, the body force appears as a term on theright-hand-side of the fluid momentum equation.

For a single dielectric barrier discharge, during one-half of the ACcycle, electrons leave the metal electrode and move towards thedielectric where they accumulate locally. In the reverse half of thecycle, electrons are supplied by surface discharges on the dielectricand move toward the metal electrode. Prior research studied thespace-time evolution of the ionized air light-emission over a surfacemounted SDBD plasma actuator. During the negative-going half cycle, theelectrons originate from the bare electrode, which is essentially aninfinite source that readily gives them up. In the positive-going halfcycle, the electrons originate from the dielectric surface. Theseapparently do not come off as readily, or when they do, they come in theform of fewer, larger micro-discharges. This asymmetry plays animportant role in the efficiency of the momentum coupling to theneutrals. The result is that the intra-AC-cycle body force occurs in twoshort durations, with that associated with the electrons leaving theexposed electrode being much larger than that when they leave thedielectric surface. This is often referred to as a “big push” and“little push”. AC waveforms such as a saw-tooth can maximize thebig-push portion.

As shown in the schematic for the pulsed-DC plasma actuator in rightpart of FIG. 6, the DC source 212 is supplied to both electrodes 202,204. A resistor, R, limits the current to the lower electrode, which isalso connected to a fast-acting solid-state switch that when closed,shorts the voltage to the lower electrode to the power supply ground. Aperiodic trigger signal consisting of a TTL pulse is supplied toactivate the solid-state switch 210.

A picture of an example assembled circuit is shown in FIG. 7 which showsan inductive current sensor 402 and a high voltage probe 404 as part ofa test setup for the actuator. Also visible in the photograph are theinductive current sensor 402 (Pearson Model 2100) seen as the thick ringin the background, and the high voltage probe 404 (LeCroy Model PPE 20kV) seen in the upper right corner. These were used to record currentand voltage time series supplied to the actuator. Analysis of these timeseries was used to correlate its effect on the thrust performance of theactuator. The high-voltage DC power supply 212 used for theseexperiments is a Glassman, Model PS/PH050R60-X18 with a maximum voltagerating of 50 kV, and maximum current limit of 60 mA. The thrustgenerated by the plasma actuator 20 was measured by mounting theactuator on an electronic force measuring scale.

An example of the simultaneously captured voltage and current timeseries for one of the plasma test plates is shown in FIGS. 8A-8B. Thiscorresponds to a supply voltage, VddH=4 kV and a pulsing frequency of512 Hz. The lower plot shows the voltage time series measured at thecovered electrode. This represents the output of the high-speedsolid-state switch 212. FIG. 8A corresponds to the corresponding currenttime series that was measured at the exposed electrode. FIG. 8Bcorresponds to the corresponding voltage time series that was measuredat the exposed electrode.

Experiments have been performed to document the induced thrust producedby the example DBD plasma actuator. For this, the plasma actuatorconsisted of electrodes that were 2.5 in. in length. The dielectriclayer consisted of two, 2 mil. thick layers of Kapton film. The actuatorwas operated either with an AC input or with a pulsed-DC input. The twoapproaches were categorized in terms of the amount of induced thrustproduced by the two plasma actuator arrangements. The improved resultsare shown in the chart of FIG. 9.

There are two notable features with the AC plasma actuator operation.The first is that the thrust increase with input voltage displays thecharacteristic power law relation namely, T˜V³⁵. The second feature isthat the generated thrust is significantly less than that of thepulsed-DC operation. The advantage of the pulsed-DC plasma actuator forthe present research is its ability to decouple the air ionizationgeneration, produced by the short duration short of the coveredelectrode, with that of the voltage control, which is set by the DClevel applied to the two electrodes. In contrast, the AC-DBD approachhas only one control: voltage. As a result, the pulsed-DC approach hasthe potential to localize the spanwise blowing effect and affect to thenear-wall region of the turbulent boundary layer. Furthermore, the lowerrequired power of the pulsed-DC approach is favorable in terms ofachieving a net drag reduction that includes the power to the actuator.

Extensive discussions have been held between team members and interestedparties at NASA. One of the most discussed issues has been the physicsbehind the pulsed-DC actuator's low power usage relative to the earlierAC-DBD designs. The optimized Pulsed-DC DBD power configuration ismanifest as a short duration current pulse in a longer transient,decaying electric field. The short current pulse acts to both ionize andtransfer an initial increment of momentum to the air. Following thepulse, when the measured external current is zero, remaining ionscontinue to be accelerated by the decaying DC electric field. The energyresponsible for this additional momentum transfer is fully accounted forby the initial current pulse. After a delay time determined by the RCtime constant consisting of the actuator capacitance C and isolationresistor R, the cycle is repeated. After sufficient pulses, anequilibrium induced-flow amplitude is reached, based on air properties,voltage amplitude and decay rate, and pulse width and frequency.Compared to the conventional AC-DBD, the Pulsed-DC DBD creates only theminimum ions required to accelerate the air, resulting in much higherelectrical-to-kinetic energy conversion efficiency. Compared to thenano-pulse DBD that creates solely a scalar pressure and temperatureperturbation, the pulsed-DC DBD retains directional momentum transferreadily adaptable to flow control applications. This is consistent withall of the experimental observations.”

The design of the plasma plates 42 (shown below in FIGS. 14A-B) wasbased on a mechanism for turbulent boundary layer drag reduction theinvolved introducing a spanwise velocity component near the wall. Thevelocity component could be uniform in one direction or opposingdirections, however for drag reduction it needed to be confined to theboundary sublayer and buffer layer, y⁺≤S100.

The parameters for the design were based on a combination of experimentsthat were performed on test samples. These tests needed to confirm thewidth of exposed electrodes and spacing between covered electrodes thatwere needed to prevent plasma from forming in unintended regions. Thewidth of the covered electrode was also a parameter since it provided alength over which the actuator induced velocity developed. The width andspacing of electrodes, which were largely based on the plasma actuatorphysics, also impacted the design for drag reduction, since when put interms of boundary layer spanwise wall units, z+, needed to be in therange, of the order of 400-500, that was thought to be optimal in theliterature. Table 1 shown in FIG. 10 provides some reference lengthsbased on the expected boundary layer conditions at the location of theplasma plate for M=0.1. Of particular interest is the z+ extentcorresponding to a physical spacing of the design of the plasma plateswas based on a mechanism for turbulent boundary layer drag reduction theinvolved introducing a spanwise velocity component near the wall. Thevelocity component could be uniform in one direction or opposingdirections, however for drag reduction it needed to be confined to theboundary sublayer and buffer layer, y+:S100.

This design of the plasma plates involved using a 3 mil. thick Ultemfilm as the dielectric layer. Ultem has a dielectric strength of 5kV/mil., which is comparable to Kapton. However, in contrast withKapton, Ultem is not affected by the ozone generated by the plasma thatlimits the operating life of Kapton film. Various plasma actuators werefabricated using the Ultem to examine the minimum width of exposedelectrodes and spacing between covered electrodes to prevent plasma fromforming on the edge of the exposed electrode that was not facing thecovered electrode. The minimum width of the exposed electrode was foundto be 1.6 mm. The minimum spacing between the covered electrodes wasfound to be 4.8 mm.

The last task needed in the design of the plasma plate was to determinethe width of the covered electrode. This involved performing velocitymeasurements over the covered electrode. The object was to determine howthe maximum induced velocity from the plasma actuator developed withdistance from the exposed electrode. A photograph of the experimentalsetup is shown in FIG. 11A. It consisted of a glass total pressure probe40. The glass probe was fabricated from a hollow glass tube with a0.0625 mm O.D. that was heated at one end and stretched to form a sharppoint. The point was broken off to leave a small opening. The taperedtip of the glass probe is best viewed in the side-view photograph inFIG. 11B. The glass probe was mounted to a two-axis micrometertraversing mechanism that was manually operated. The glass totalpressure probe was connected to one side of a Validyne differentialpressure transducer with a diaphragm that provided a full-scale pressurerange of 12.7 mm of water. The other side of the differential pressuretransducer was open to the atmosphere in the lab. The voltagesproportional to pressure were acquired with a digital computer andconverted to velocity.

Examples of the velocity profiles in physical velocity units, measuredat the closest (4 mm) and furthest (24 mm) distances from the edge ofthe exposed electrode are shown in FIG. 11. This was for the pulsed-DCplasma actuator operating with a DC voltage of 10 kV and a pulsingfrequency of 500 Hz. Velocity profiles like those shown in FIGS. 12A-12Bwere used to document the peak velocity and the distance of the peakvelocity from the surface as a function of the distance from the exposedelectrode. The results are shown in FIGS. 13A-13B. The peak velocitydecays approximately linearly with distance from the exposed electrode.The left axis shows the velocity in physical units. The fight axis showsthe peak velocity normalized by our nominally expected u_(r) for theboundary layer at Mach 0.1 that was given in Table 1 shown in FIG. 10.With u_(r)=1 being a rough threshold for effect, this indicates that adistance of approximately 20 mm is the maximum useful dimension of thecovered electrode.

FIG. 13B shows the location of the peak velocity from the surface as afunction of the distance from the exposed electrode. The left axis isthe physical height. The right axis indicates the height of the velocitypeak normalized by the nominally expected, y at y+=100 for the boundarylayer at Mach 0.1 that was given in Table 1 shown in FIG. 10. Now y+=100is considered to be the edge of the buffer layer in a turbulent boundarylayer. Based on these results, the peak velocity is only confined tothat region up to 4 mm. from the exposed electrode.

Based on these results, two plasma plate designs were fabricated.Top-view schematic drawings of the two designs for the plasma plate 42are shown in FIGS. 14A-14B, where all dimensions are in millimeters. Ineach, the plasma plate 42 exhibits a series of plasma actuators 12arranged in ordered rows. The plasma actuators are so ordered to focusand direct their velocity inducing effect into a unified control of thevorticity of the fluid flow around the wall.

The outer edge in each design matches the 9 in. (228.6 mm) square sizeof the measurement plate. The schematics show the outlines of thecovered electrodes as well as the locations of the exposed electrodeswhen placed on one edge of the covered electrode for the “spanwiseblowing” configuration. In the design for the plasma plate 42 in FIG.14A, the width of the covered electrode is 16 mm. The design for theplasma plate 42 shown in FIG. 14B has covered electrodes with a width of24 mm. In each case the width of the covered electrode is the minimum 2mm found by the bench-top experiments to prevent plasma from forming onthe opposite edge from the covered electrode. Similarly, the spacingbetween the covered electrodes was 7 mm so that the spacing between theedge of the neighboring covered electrode and the next exposed electrodewas the 5 mm found to be needed to also prevent unwanted plasma fromforming. The covered electrodes were connected in parallel by a commonbus line located in the bottom part of the schematics.

The pattern for the covered electrodes and their connection bus 22 weremachined into a 6.35 mm thick sheet of Gil Garolite. This produced arecess for the 4 mm thick copper foil tape (2 mm thick copper and 2 mmthick glue layer) used for the covered electrode and connection bus 22.

This allowed a smooth surface on which the dielectric film was applied.The dielectric was a continuous sheet of 3 mm thick Ultem that wasglue-backed. The exposed electrodes were also fabricated from the copperfoil tape. The pattern was applied to the surface of the Ultem film. Aconnection bus that was similar to that of the covered electrode wasused to distribute the power to the exposed electrodes. FIG. 15A shows aphotograph of the fully assembled plasma plate with 16 mm coveredelectrodes showing the linear ordered rows of plasma actuators 20. Eachassembly was mounted onto a flat honeycomb plate that was designed to beheld in the drag force measurement setup. These honeycomb plates werepreviously used to measure baseline drag in a separate ongoing studyperformed with the NASA Langley Acoustic Lining Team. FIG. 15B shows theplasma plate 42 while operating with the pulsed-DC on a bench-top in adarkened lab.

The plasma plate assemblies were mounted to the drag force measurementsetup in the wind tunnel. A photograph of the plasma plate 42 with 16 mmcovered electrodes and exposed electrodes located on the edge of thecovered electrode is shown in FIG. 16. This is viewed looking in thedownstream directions towards the exit of the test section. The powerbus for the exposed electrodes is on the downstream back edge of theplasma plate to minimize any flow disturbances it might produce. Thepower to the plasma plate was supplied through two 30 gauge coated wireleads, with one each connected to the covered and exposed electrodepower bus. These thin wires are visible on the right side of thephotograph. The thin wires were chosen to produce a minimum amount ofdrag on the plasma plate.

As previously indicated, two plasma plate designs were fabricated thathad covered electrode widths of 16 mm and 24 mm. Configurations of theplasma plate are detailed in the Tables 2-5 shown in FIGS. 17A-17D. Witheach of these there were two exposed electrode configurations. In one,the exposed electrode was located on the edge of the covered electrodeto produce uniform spanwise blowing. In the other configuration, theexposed electrode was located in the spanwise center of the coveredelectrode. This arrangement would produce opposing spanwise blowing witha stagnation line in the space between neighboring covered electrodes.These configurations are summarized in Table 2 shown in FIG. 17A.

In each of the four configurations, the free-stream Mach number wasvaried from 0.05 to 0.12. At each Mach number, the plasma panel wasoperated at DC voltages from 4 kV to 8 kV. In all cases the pulsingfrequency was 512 Hz. For each experimental condition, the output fromthe drag-measuring load cell was continuously acquired for a period oftime that was sufficient to calculate a stable time-averaged (mean)value. This was typically a 30 second average. The output from the loadcell was also acquired with the plasma plate operating without flow. Theaverage reading without flow was then subtracted from the reading withflow to ensure that the drag reading with the plasma plate operatingwith flow did not include any effect of electronic noise. This processwas performed for every one of the plasma plate operating voltages.

The power delivered to the plasma plates in each of the fourconfigurations at all of the voltages was determined using a 500 MHzLecroy digital oscilloscope to acquire the voltage and current timeseries. The voltage was measured using a Lecroy high voltage probe thatwas connected to the power lead to the covered electrode. The currentwas measured using an inductive current sensor that was located on thepower lead to the exposed electrode. The time series from both sensorswere stored and post-processed. This is the time series that was shownin FIG. 8. This is representative of all of the time series at all ofthe voltages used in the experiment.

Analysis of the voltage and current traces indicates that except withinthe current pulse, the current is zero. During the current spike, thevoltage potential is the maximum DC level. If the period during thecurrent peak is expanded in time, the width of the pulse can bedetermined.

This represents the duty cycle of the periodic process. Table 4 shown inFIG. 17C lists the DC pulse widths based on the current traces, and thecorresponding duty cycle percentage of the 512 Hz pulsing frequency forthe four plasma plate configurations for the range of voltages used inthe experiments. The method of calculating power then consisted oftaking the product of the peak current, peak voltage, and duty cycle.Table 4 summarizes the power delivered to the four plasma plateconfigurations for the range of voltages used in the experiments. Thepower is measured Watts as well as the power normalized by the totallength of the generated plasma, which for the edge configuration isassumed to be the total length of the electrode times the number ofexposed electrodes. This length is doubled for the centered electrodes,since in that case the plasma was generated on both sides of the exposedelectrode.

The following provides a design for the pulsed-DC plasma actuator dragreducing plate for Mach numbers up to the 0.6 maximum of the Notre DameMach 0.6 wind tunnel. The design is based on the same 228.6 mm (9 in.)square plate that was used in the Phase I experiments.

Based on the Phase I experiment, the optimum spacing of the plasmaactuator exposed electrodes corresponds to a z−=1000. The physicalspacing scales with Mach number as M^(−0.92), therefore the spacingdecreases with increasing Mach number. These are given as a function ofMach number in the second column of Table 5. The Phase I experimentsvalidated that the pulsed-DC actuator provided the control to allow useof the centered electrode configuration. This configuration scales downmore easily than the spanwise blowing configuration because (1) it canbe applied over a single covered electrode and (2) the effectiveelectrode spacing is twice the z+=1000 requirement, meaning theelectrodes can be placed twice as far apart compared to the spanwiseblowing arrangement. Column 3 in Table 5 gives the centered electrodespacing as a function of Mach number. Based on the spacing betweenelectrodes at each Mach number, Column 4 in the table gives the numberof electrodes in the spanwise direction that would cover the 228.6 mmsquare plate (leaving a border of approximately 15 mm). The plasma willform on both sides of the exposed electrodes. Therefore the length ofplasma corresponds to twice the length of each exposed electrode timethe number of electrodes. The total plasma length as a function of Machnumber is given in Column 5 of Table 5.

Table 4 lists the power-per-meter length for each of the electrodeconfigurations of the plasma plate 42. The average W/m of the fourconfigurations at a DC voltage of 6 kV was used to estimate the requiredpower to the actuator as a function of Mach number. The optimum voltagein the Phase I experiments was found to be between 5 kV to 6 kV. Thatoptimum voltage was not found to be sensitive to the Mach number. Thisis consistent with one of the physical interpretations that the walllongitudinal streaks are the result of an instability, in which a smallvelocity perturbation is sufficient to disrupt their formation. Column 6in Table 5 then lists the plasma actuator power based on the 6 kVaverage W/m of pulsed-DC plasma.

The drag on the 228.6 mm square plasma plate 42 at its Phase I locationin the test section for the naturally developing turbulent boundarylayer was estimated for the range of Mach numbers 0.1 to 0.6. The powerassociated with the drag is listed in Column 7 of Table 5. The dragpower scales as M³ so that it is dramatically increasing with Machnumber. If it is assumed that the 60% drag reduction observed in Phase Iwas achieved at all of the Mach numbers in the table, then Column 8lists the power associated with 60% of the drag. The net power reductionis then the ratio of the power in 60% of the drag on the plate, dividedby the estimate of the power supplied to the plasma plate. This is theratio of the values in Columns 8 and 6. The result is given in Column 9of Table 5. The values in Column 9 are plotted as a function of thefree-stream Mach number in FIG. 16. The estimates are remarkable withthe potential of a 4500% net drag reduction at Mach 0.6. Even if theestimates of the plasma power were off by an order of magnitude, the netdrag reduction would still be an impressive 450%.

In summary, the spacing between the electrodes and the powerrequirements for the 228.6 mm square plate are easily feasible tofabricate and test at Mach numbers up to 0.6 in the Phase II.

This section presents the results of a series of experiments performedin the Notre Dame Mach 0.6 wind tunnel that is focused on thedemonstration of turbulent boundary layer skin friction drag reduction.The experiments are performed in a zero pressure gradient (ZPG) fullyturbulent boundary layer for a range of incompressible Mach numbers.Relevant boundary layer parameters are provided in Table 6. Fouractuator designs are considered and the focus of each is to intervene inthe streak transient growth instability (STGI) mechanism that forms thebasis for the self-sustaining mechanism of wall turbulence production.Two of the actuator designs use the body force produced by a low power,new revolutionary actuator to create a unidirectional spanwise flow inthe near-wall region of the ZPG boundary layer in order to smooth lowspeed streaks and thereby prevent STGI. As noted previously, thesediffer only in terms of surface inter-electrode spacing (16 mm and 24mm). The second design uses the new revolutionary actuator with anelectrode arrangement that produces a series of spanwise opposed walljets that are confined to the near-wall region. Again, the focus of theflow control strategy was to smooth low-speed streaks and therebyprevent STGI.

FIG. 18 presents two sample baseline drag measurements without plasmaflow control. These baseline measurements give an indication of the highlevel of repeatability of the drag measurements as well as theirexpected variation with M as evidence by the quadratic fit (dashedline). Furthermore, trial 1 was obtained with the 24 mm unidirectionalactuator installed and trial 2 with the 24 mm opposed wall jet actuator.The agreement with the analysis shown in FIG. 1 indicates that thesurface electrodes were sufficiently hydrodynamically smooth so as tohave negligible effect on skin friction drag.

The following sections summarize the results of revolutionary newactuator based drag reduction experiments for both the unidirectionaland opposed wall jet actuators.

FIGS. 19A-19B presents the measured percentage change in skin frictiondrag as a function of applied voltage for the 16 mm opposed wall jetactuator (i.e. centered surface electrode). Experimental results overthe freestream Mach number range 0.05<M_(∞)>0.1 are shown. FIG. 19Apresents results for the untripped approach boundary layer case. FIG.19B presents results with the approach boundary layer thickened by asmall rectangular trip placed 2.2 m upstream of the actuator leadingedge. The primary effect of the trip was to approximately double thethickness of the approach boundary layer (e.g. from δ=44 mm toδ_(trip)=99 mm at M_(∞)=0.05) which also had the intended effect ofincreasing the near-wall low speed streak spacing. FIG. 19A shows thatskin friction drag reduction occurs at each Mach number for an appliedactuator voltage of 6 kV. The applied actuator voltage being thedifference between the voltage at the covered electrode and the voltageat the exposed electrode. A maximum drag reduction of 23% occurs forM_(∞)=0.06 with smaller reductions occurring at higher Mach numbers. Itis important to note that the effect of the actuation is to increasedrag for all Mach numbers with higher applied voltages of 7 kV or 8 kV.This is likely due to local upwelling s that are generated by thecolliding wall jets at the highest applied voltages. This would serve tosignificantly increase the production of wall-normal component vorticitythrough increased spanwise near-wall velocity gradients, ∂U/∂z, andthereby promote STGI. Thus, unlike separation control applications whereincreased actuator authority generally has a positive effect, FIG. 19Ashows that STGI control is very sensitive to applied voltage. FIG. 19Aalso shows increased drag at the lower applied voltage of 5 kV. It isspeculated that this is due to the opposing wall jets havinginsufficient authority to smooth low speed streaks (as in the 6 kV case)and instead promoting spanwise inhomogeneity of the streamwise velocitythrough a localized wall jet influence near each surface electrode. FIG.19B presents the percent change in skin friction drag with the approachboundary layer boundary layer tripped. Again, drag reduction occurs atall Mach numbers for an applied actuator voltage of 6 kV but thereductions are much larger; up to nearly 70% at M_(∞)=0.05. Although thepercent drag reduction decreases systematically at higher Mach numbers,it remains significant even at the highest Mach number; 17% atM_(∞)=0.1. As in the untripped case, higher applied voltages give riseto significant drag increases due to upwellings from energetic collidingwall jets. Unlike the untripped case shown in FIG. 19a , lower levels ofdrag reduction also occur at 5 kV.

In order to address the systematic variation in drag reduction with Machnumber noted for the 6 KV actuation cases shown in both FIG. 19, FIG. 20presents the percent drag reduction as a function of the (calculated)number of viscous wall units (v/u_(τ)) between the surface electrodes.

This figure shows that the greatest drag reduction occurs when theinter-electrode spacing encompasses 800-1000 wall units, which wouldcorrespond to the control of 8-10 low speed streaks. For aninter-electrode gap equal to 2000 wall units (i.e. 20 low speed streaks)drag reduction is nearly lost. The dashed line in FIG. 20 shows that thepercentage drag reduction varies approximately logarithmically withinter-electrode streak spacing.

FIGS. 21A-21B presents the measured percentage change in skin frictiondrag as a function of applied voltage for the 24 mm opposed wall jetactuator (i.e. centered surface electrode). As before experimentalresults over the freestream Mach number range 0.05<M_(∞)>0.1 are shown.FIG. 21A presents the results for the untripped TBL. The drag reductionbehavior is qualitatively similar to that shown previously for the 16 mmopposed wall jet case. Drag reduction occurs for applied voltages of 5and 6 kV with increased drag occurring at the highest voltages of 7 and8 kV. As described previously, this drag increase is likely due toupwellings generated by colliding spanwise wall jets that serve topromote STGI. Peak drag reduction is 47% at M_(∞)=0.05 and 5 kV appliedvoltage. However, drag reductions of approximately 20% are noted forM=0.06 and 0.07 for applied voltages 5 and 6 kV, respectively. Even atM_(∞)=0.1 the drag reduction is 7% at 5 and 6 kV. FIG. 21B presentsexperimental results for the tripped TBL. Overall the drag reductionperformance is improved by the tripping and this shows that this isassociated with a reduction in the number of low-speed streaks betweensurface electrodes. Peak drag reduction is 47% at M_(∞)=0.05 for the 6kV case. Comparison of FIG. 21A and FIG. 21B show that drag reduction athigher Mach numbers is greater for the tripped case. For example, thedrag reduction is 36% at M_(∞)=0.08 for 5 kV applied voltage. Reductionsin excess of 20% are observed for M_(∞)=0.06 and 0.07. As before thehighest applied voltages show a detrimental effect with significantincreases in drag (e.g. nearly 40% at M_(∞)=0.05 for 7 and 8 kV).

FIG. 22 presents the percent drag reduction as a function of the(calculated) number of viscous wall units (v/u_(τ)) between the surfaceelectrodes for the 24 mm opposed wall jet case. This figure shows thatthe greatest drag reduction is associated with approximately 1000 wallunits between the surface electrodes (i.e. control of 10 low-speedstreaks). As the number of low-speed streaks between surface electrodesincreases the percent drag reduction is diminished, varyingapproximately logarithmically. For 20-25 low speed streaks, dragreduction is reduced to between 5-10%

FIGS. 23A-23B presents the measured percentage change in skin frictiondrag as a function of applied voltage for the 16 mm unidirectionalspanwise wall jet actuator. Experimental results over the freestreamMach number range 0.05≤M_(∞)≤0.125 are shown. The untripped TBL case isshown in FIG. 23A. This figure shows that unidirectional spanwise walljets are also capable of producing drag reduction which occurs for the 6kV applied voltage. Maximum drag reduction of 24% is measured for bothM_(∞)=0.05 and 0.06 with lesser amounts at higher Mach numbers. Theactuation is shown to increase drag at both the lowest and highestapplied voltages tested. The increase at 5 kV is possibly due toinsufficient wall jet velocity which provides a near-electrode localizedcontrol effect that gives rise to spanwise gradients, v/u_(τ), acrossthe inter-electrode gap that promotes STGI. At the highest voltage thewall jet likely is not confined to the near-wall region across theentire inter-electrode gap, thereby increasing drag. Significantincreases in drag are shown to occur for 7 kV applied voltage.

FIG. 23B presents experimental results for the 16 mm unidirectionalactuator with the tripped TBL. Peak drag reduction is now much greaterthan in the untripped case and occurs at the lower applied voltage of 5kV. Peak drag reduction is 58% at M_(∞)=0.05 and 51% at M_(∞)=0.06 withvalues between 16% and 4% at the higher Mach numbers.

FIG. 24 presents the percent drag reduction as a function of the(calculated) number of viscous wall units (v/u_(τ)) between the surfaceelectrodes for the 16 mm unidirectional wall jet case. In both trippedand untripped cases, the degree of drag reduction is again reduced asthe number of wall units between the electrodes grows. The largest dragreduction occurs around 1000 wall units (i.e. ten low-speed streaks) aswas the case for the opposed wall jet actuators.

FIG. 25A-25B presents the measured percentage change in skin frictiondrag as a function of applied voltage for the 24 mm unidirectionalspanwise wall jet actuator. Experimental results over the freestreamMach number range 0.05≤M_(∞)≤0.1 are shown. The untripped TBL case isshown in FIG. 25A. The only drag reduction in this case occurs at thelowest applied voltage of 4 kV and does not exceed 11% which occurs forM_(∞)=0.08. Comparison with FIG. 23A indicates that the 24 mmunidirectional actuator is not as effective as the 16 mm version. Thissuggests that the unidirectional actuators will function best with smallsurface inter-electrode gaps. The tripped TBL case is presented in FIG.25B. Maximum drag reduction now occurs at 6 kV but does not exceed 11%.

The new revolutionary actuators were examined in terms of not onlypercent drag reduction but also in terms of power savings versus powerinput to the actuators. The goal was to determine if the actuators werecapable of achieving net power savings.

The power savings due to the plasma actuator, ΔP, is given by,M _(∞) =ΔP=P _(off)(DR)  (1)

Where P_(off)=D_(off)V_(∞) is the power lost due to skin friction dragwith the actuator off and DR is the fractional drag reduction due to theactuator. Denoting the power input required to operate the actuator asP_(in) for net power savings, it is required that

$\begin{matrix}{\frac{\Delta\; P}{P_{IN}} = \frac{P_{off}({DR})}{P_{IN}}} & (2)\end{matrix}$

Of course the best one could achieve would be to have 100% dragreduction in which case (2) becomes,

$\begin{matrix}{\frac{\Delta\; P}{P_{IN}} = \frac{P_{off}}{P_{IN}}} & (3)\end{matrix}$

As an example, this quantity was calculated for the opposed wall jetactuator and is plotted in FIG. 26. This figure shows (1) that at agiven Mach number the maximum potential power savings decreases rapidlywith applied voltage and (2) at fixed voltage, maximum benefit in termsof net power savings occurs at higher Mach number. In order to calculatethe net power savings the values shown in FIG. 26 need only bemultiplied by the appropriate values of the fractional drag reduction.As an example, FIG. 27 presents net power savings, ΔP/P_(IN) as afunction of Mach number for the 16 mm opposed wall jet actuator operatedat 6 kV with the TBL tripped. Although the drag results shown previouslyin FIG. 19B are most impressive at the lower Mach numbers, FIG. 27 showsthat the net power savings actually occurs between M_(∞)=0.072 and0.095.

FIG. 28 presents net power savings, ΔP/P_(IN) as a function of Machnumber for the 24 mm opposed wall jet actuator operated at 5 kV with theTBL tripped. Again there is significant net power savings and it occursat the higher Mach numbers; in this case over the approximate Machnumber range 0.072<M_(∞)<0.097

FIG. 29 presents ΔP/P_(IN) as a function of Mach number for the 16 mmunidirectional wall jet actuator operated at 5 kV with the TBL tripped.Due to the very large drag reduction shown in number range0.072<M_(∞)<0.097.

Both the new unidirectional and opposed wall jet actuator designs havebeen found capable of smoothing near-wall low speed streaks to intervenein the STGI mechanism responsible for the self-sustaining mechanism ofnear-wall turbulence production. As a consequence, very significantreduction in skin friction drag has been observed. The opposed wall jetactuator has produced drag reduction of over 65% while theunidirectional spanwise wall jet actuator has realized up to 58% dragreduction. Perhaps most significant is the demonstration of significantnet power savings; the power gain through drag reduction (especially atthe higher Mach numbers) has been shown to significantly exceed thepower input to the actuator for both actuator designs. This is aconsequence, in part, of the comparatively low power required in theoperation of the new actuator.

Unlike separation control applications where increased actuatorauthority is generally beneficial, STGI control is shown to be verysensitive to applied voltage (i.e. plasma induced wall jet velocity)with applied voltages both above and below that associated with optimumdrag reduction capable of producing significant drag increases. This islikely associated with wall jet velocities that increase spanwisenear-wall velocity gradients, ∂U/∂z, which augments wall-normalvorticity and thereby exacerbates the STGI mechanism.

Comparison of tripped and untripped flow control cases demonstrates thatdrag reduction for both actuator configurations is generally optimum fora spanwise inter-electrode spacing of approximately 1000 viscous wallunits or, equivalently, the control of ten low-speed streaks. Forinter-electrode spacing approaching 2000 viscous wall units (20low-speed streaks) the drag reduction is greatly reduced.

FIG. 30 presents the projected percentage net power savings as afunction of M_(∞) for the range of fractional drag reductionsrepresentative of those achieved in the reported experiments for the 24mm configuration. This figure shows that ΔP/P_(IN) varies approximatelyquadratically with increasing M_(∞). Note that even if P_(IN) was anorder of magnitude larger than estimated, the net power savings atM_(∞)=0.6 would still be 80% and 450%, respectively, for fractional dragreductions of DR=0.1 and 0.6.

In the course of this disclosure, the constraints on the design of thebody force field can be summarized in the following ways: 1) the effectof actuation should be kept within the laminar sub-layer; 2) at tunnelconditions, the total force should be 150 mN/m (based on themeasurements in the Notre Dame tunnel, 3) the force should be strongestat the junction between the covered and exposed electrodes; 4) based onconventional plasma actuators, the body force should drop away veryquickly over the covered electrode, and more slowly over the exposedelectrode; 5) the force field should induce a normal velocity componenttoward the wall above the junction between the covered and exposedelectrodes; 6) the force field should induce a spanwise velocitycomponent away from the electrode junction over the exposed electrode,7) the force field was set to act in the wall-normal direction about 30%as strongly as in the spanwise direction; 8) since the channelconditions were different than those in the tunnel, the body force isscaled by the ratio of dynamic pressures.

Using the above constraints, the following Gaussian function wasdeveloped to model the body force magnitude:

$\begin{matrix}{F = {A\;{\exp\left( {- \left( {\frac{\left( {z - z_{0}} \right)^{2}}{2*\sigma_{z}^{2}} + \frac{\left( {y - y_{0}} \right)^{2}}{2*\sigma_{y}^{2}}} \right)} \right.}}} & (4)\end{matrix}$

In the above expression, y₀ and z₀ represent the origin of the bodyforce function. For the current work, this was taken to be 0.001 mnormal to the actuator electrode junction. Based on the mean velocityprofiles in the baseline case, the value for σ_(y) was chosen as:σ_(y)=0.00035  (5)

The value used for σ_(z) depended on the spanwise position of the givenpoint relative to the location of the electrode junction. A base valuewas defined using the spanwise width of the domain such that thefunction would have non-trivial values over roughly a quarter of thespanwise extent:

$\begin{matrix}{\sigma_{z} = \frac{W}{4\sqrt{2\ln\; 10}}} & (5)\end{matrix}$

If a point was in a region on the exposed electrode side of thejunction, then this base value would be used as σ_(z). If the point wason the covered electrode side of the junction, then σ_(z) was taken tobe a tenth of σ_(z) ₀ . The magnitude of the function was chosen suchthat integrating it over a meter in the streamwise direction for all theactuators on a given channel wall would yield a total body force of 150mN (note that the actuators did not actually extend for a full meter inthe simulation). The amplitude was thus taken to be:

$\begin{matrix}{\sigma_{z} = \frac{F_{mag}}{{\pi\sigma}_{y}\sigma_{z}}} & (5)\end{matrix}$

The force magnitude F_(mag) was computed using numerical integration ofthe Gaussian function over the channel cross-section and scaling theresult to match the desired total actuation force of 150 mN/m on eachwall. Once this magnitude was computed, the actual value used in thesimulations was further scaled by the ratio of dynamic pressures betweenthe simulation conditions and the tunnel conditions.

Two plasma actuators were modeled on each wall of the channel, in anopposed configuration (and mirrored top to bottom). Actuators wereplaced at 10% span and 60% span, with the orientation such that theinduced velocity would push toward the center of the domain. The bodyforce was active only in the upstream half of the flow domain. A plot ofthe body force magnitude of a single actuator is shown below in FIG. 31.As the figure shows, this body force is centered at 10 percent of spanand is oriented in the direction of positive z. Thus, it is expectedthat flow will be drawn down from above the electrode junction andaccelerated to the right of it.

To test that the body force field was producing the expected qualitativeresponse, a quick test case was run using a much reduced domain withquiescent flow. After a short simulation, the contours of the spanwiseand wall-normal velocity components were examined. The results areplotted in FIG. 32 and FIG. 33. As the figures show, the flow isbehaving exactly according to the intended design, with flow being drawndown above the two actuators (the mirroring actuators on the top wallare not visible in the plots) and ejected toward the center of thedomain.

The plasma body force discussed above was applied to a turbulent channelflow simulation. Even in this early stage of the simulation, however,the impact of the actuation is beginning to be seen in some quantities.FIG. 34 and FIG. 35 show profiles of the mean spanwise velocity and thestreamwise turbulent velocity fluctuations across the channel. At thisearly point in the actuated simulation, no significant change from thebaseline case is apparent. The same is true for the u-v fluctuationcorrelations in FIG. 36.

Some differences become apparent when looking more closely at theactuated region. A plot of the instantaneous turbulent velocityfluctuations along a wall-normal line passing through a region where thebody force is active are shown in FIG. 37. As can be seen from thescaling of the horizontal axis, this plot is tightly zoomed into thenear-wall region. A distinct impact of the actuation on the spanwise andvertical velocity components is apparent, however.

To get a more complete picture of the impact of actuation on the flow,the components of velocity vector were compared between the baseline andactuated cases. Contours of these differences are plotted in FIG. 38 andFIG. 39. These plots are zoomed in on one of the four regions ofactuation in the channel flow. As can clearly be seen, the same basicpattern of fluid being drawn down from above and ejected to the side ispresent. The magnitude of the differences between the solutions has beenrapidly growing as the body force takes effect. The peak value of thespanwise velocity difference now approaches half of the frictionvelocity (the experimentally observed values are on the order of one totwo times the friction velocity).

Some surfaces of stream wise vorticity are shown in FIG. 40. At thisearly stage of the actuated simulation, no significant disruption of thepattern seen previously in the baseline cases is seen. As the impact ofthe body force propagates throughout the domain differences may arise.As shown above, the disclosure has demonstrated a capability to captureimportant aspects of the impact of plasma actuation. While thesimulations have not had time to advance far enough to assess the fulleffect on drag, all the necessary infrastructure has been put in placeto do so.

Drag reduction was able to be achieved at all the conditions tested, andwith all the actuator configurations. The maximum drag reduction of morethan 65 percent observed in the turbulent flat plate boundary layer farexceeds the capabilities of any other technology. Even when accountingfor the power required to drive the SLIPPS system, net drag reduction ofmore than 50 percent was observed in some cases.

The SLIPPS drag reduction technology clearly has the potential to have amajor impact on the efficiency of a wide array of air vehicles, raisingthe possibility of longer ranges, heavier payloads, reduced fuel costs,and less greenhouse gas emissions.

Although certain example methods and apparatus have been describedherein, the scope of coverage of this patent is not limited thereto. Onthe contrary, this patent covers all methods, apparatus, and articles ofmanufacture fairly falling within the scope of the appended claimseither literally or under the doctrine of equivalents.

We claim:
 1. A plasma actuator array comprising: a plurality of plasmaactuators positioned on a surface, each plasma actuator comprising: adielectric; a first electrode exposed to a fluid flow, the fluid flowhaving a boundary layer with a boundary layer mean flow direction; asecond electrode separated from the fluid flow by the dielectric; apulsed direct current power supply providing a first voltage to thefirst electrode and a second voltage to the second electrode; and a busoperably connected to distribute power to the plasma actuators,positioned to minimize flow disturbances; wherein the plasma actuatorsare arranged into a series of linear rows, each of the linear rowsaligned parallel to the boundary layer mean flow direction, such that avelocity component perpendicular to the boundary layer mean flowdirection is imparted to the fluid flow close to the surface, andwherein the exposed first electrode is adapted to produce opposingspanwise blowing with a stagnation line in the space between neighboringcovered second electrodes.
 2. The plasma actuator array of claim 1wherein the plasma actuators are arranged to produce a reduction in theviscous drag of the fluid flow across the surface.
 3. The plasmaactuator array of claim 2 wherein the reduction in the viscous drag isaccomplished by smoothing a mean flow distortion produced by turbulentboundary layer low-speed streaks to prevent streak transient growthinstability that results in streak lift-up and the generation of higherviscous drag.
 4. The plasma actuator array of claim 1 wherein theexposed electrode is adapted to produce uniform spanwise blowing.
 5. Theplasma actuator array of claim 4 wherein the exposed electrode islocated on the edge of the covered electrode.
 6. The plasma actuatorarray of claim 1 wherein each plasma actuator further comprises: aswitch electrically coupled to the first and second electrode and to thedirect current power supply such that energization of the direct currentpower supply by action of the switch causes the fluid to generate aplasma on the surface; the plasma, having an electric field vectorproduced by the first and second electrodes resulting in a body forcevector field that induces a velocity component in the fluid in adirection parallel to the surface and perpendicular to a mean flowdirection of the boundary layer fluid flow; wherein the energizationcaused by the switch creates a repetitive pulse having a length of timeby momentarily connecting one of the first or second electrodes to aground, such that, for the majority of the pulse, the voltages of thefirst and second electrodes are at the same DC potential and no power isconsumed by the plasma actuator array.
 7. The plasma actuator array ofclaim 1 wherein the fluid flow along the surface is an attachedturbulent boundary layer.
 8. The plasma actuator array of claim 1wherein the plasma actuators are arranged to lower the viscous drag inthe turbulent boundary layer that passes over the surface covered by theactuator array.
 9. The plasma actuator array of claim 8 wherein theplasma actuator array is positioned on the surface in areas over whichattached turbulent boundary layers exist.
 10. The plasma actuator arrayof claim 1 wherein plasma actuators are arranged in a rectangularpattern to cover a portion of the surface over which an attachedturbulent boundary layer flows.
 11. The plasma actuator array of claim10 is located at anywhere the turbulent boundary layer along the surfaceis fully attached.
 12. The plasma actuator array of claim 1 wherein thedifference between the first voltage and the second voltage issufficient to form a plasma and to generate a body force that impartsmomentum to the air.
 13. A method of reducing viscous drag due toattached turbulent boundary layer fluid flow on a surface comprisingarranging an ordered series of plasma actuators, each plasma actuatorwith an exposed first electrode and a covered second electrode, to covera surface under the turbulent boundary layer fluid flow to produceopposing spanwise blowing with a stagnation line in the space betweenneighboring covered second electrodes; energizing the ordered series ofplasma actuators with a pulsed direct current power flow; imparting avelocity component to the fluid flow that is parallel to the surface andperpendicular to a mean flow direction of the fluid flow; and smoothinga distortion in the fluid flow produced by low-speed streaks to preventstreak transient growth instability and lift-up of the low-speed streaksfrom the surface and thereby to reduce viscous drag of the fluid flowacross the surface.
 14. A plasma actuator array comprising: a pluralityof plasma actuators positioned on a surface, each plasma actuatorcomprising: a dielectric; a first electrode exposed to a fluid flow, thefluid flow having a boundary layer with a boundary layer mean flowdirection; a second electrode separated from the fluid flow by thedielectric; a pulsed direct current power supply providing a firstvoltage to the first electrode and a second voltage to the secondelectrode; a bus operably connected to distribute power to the plasmaactuators, positioned to minimize flow disturbances; and wherein theplasma actuators are arranged into a series of linear rows, each of thelinear rows aligned parallel to the boundary layer mean flow direction,such that a velocity component perpendicular to the boundary layer meanflow direction is imparted to the fluid flow close to the surface,wherein the exposed first electrode is adapted to produce opposingspanwise blowing with a stagnation line in the space between neighboringcovered second electrodes.
 15. The plasma actuator array of claim 14wherein the exposed first electrode is located in the spanwise center ofthe covered second electrodes.